Two-dimensional Fermi Research Articles

Supercarbon assembly inspired two-dimensional hourglass fermion.

By using a tight-binding model, first-principles calculations, and abinitio molecular dynamics simulations, we theoretically demonstrate that the C76-Td-assembled two-dimensional (2D) honeycomb lattice is stable at room temperature and is resistant to mechanical deformation. We disclose that each C76-Td mimics a single carbon atom (geometrically and electronically); hence, it plays the role of one supercarbon. This inspires that the 2D material exhibits an exotic hourglass-like fermion at the Fermi level. Furthermore, we suggest that biaxial strains could modify the hourglass shape, including the electronic Fermi velocity, and induce magnetization. Hexagonal boron nitride can be employed as a protective layer without affecting the electronic structure of this material. This hourglass fermion has the potential to serve as a promising material for high-speed electronic devices and to bridge the gap between zero-dimensional spherical carbon clusters and two-dimensional graphene.

Ferroelectric Semimetals with α-Bi/SnSe van der Waals Heterostructures and Their Topological Currents.

We show that proximity effects can be utilized to engineer van der Waals heterostructures (vdWHs) displaying semimetallic spin-ferroelectricity locking, where ferroelectricity and semimetallic spin states are confined to different layers, but are correlated by means of proximity effects. Our findings are supported by first principles calculations involving α-Bi/SnSe bilayers. We show that such systems support ferroelectrically switchable nonlinear anomalous Hall effect originating from large Berry curvature dipoles as well as direct and inverse spin Hall effects with giant bulk spin-charge interconversion efficiencies. The giant efficiencies are consequences of the proximity-induced semimetallic nature of low energy electron states, which are shown to behave as two-dimensional pseudo-Weyl fermions by means of symmetry analysis and first principles calculations as well as direct angle-resolved photoemission spectroscopy measurements.

Unconventional Discontinuous Transitions in Isospin Systems.

We show that two-dimensional fermions with dispersion k^{2} or k^{4} undergo a first-order Stoner transition to a fully spin-polarized state despite the fact that the spin susceptibility diverges at the critical point. We extend our analysis to systems with dispersion k^{2α} and spin and valley isospin and show that there is a cascade of instabilities into fractional-metal states with some electron bands fully depleted; narrow intermediate ranges of partially depleted bands exist for α<1 or α>2. The susceptibility becomes large near each transition. We discuss applications to biased bi- and trilayer graphene and moiré systems.

Tensor renormalization group for fermions.

We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: A dimensional reduction treatment

Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: A dimensional reduction treatment

Standard translation twists and an operator-bounded energy inequality

Twist operators implement symmetries in bounded regions of the space. Standard twists are a special class of twists constructed using modular tools. The twists corresponding to translations have interesting special properties. They can move continuously an operator from a region to a disjoint one without ever passing through the gap separating the two. In addition, they have generators satisfying the spectrum condition. We compute explicitly these twists for the two-dimensional chiral fermion field. The twist generator gives place to a new type of energy inequality where the smeared energy density is bounded below by an operator. Published by the American Physical Society 2024

Effective gravitational action for 2D massive Majorana fermions on arbitrary genus Riemann surfaces

We explore the effective gravitational action for two-dimensional massive Euclidean Majorana fermions in a small mass expansion, continuing and completing the study initiated in a previous paper [1]. We perform a detailed analysis of local zeta functions, heat kernels, and Green’s functions of the Dirac operator on arbitrary Riemann surfaces. We obtain the full expansion of the effective gravitational action to all orders in m2. For genus one and larger, this requires the understanding of the role of the zero-modes of the (massless) Dirac operator which is worked out.Besides the Liouville action, at order m0, which only involves the background metric and the conformal factor σ, the various contributions to the effective gravitational action at higher orders in m2 can be expressed in terms of integrals of the renormalized Green’s function at coinciding points of the squared (massless) Dirac operator, as well as of higher Green’s functions. In particular, at order m2, these contributions can be re-written as a term ∫ e2σσ characteristic of the Mabuchi action, much as for 2D massive scalars, as well as several other terms that are multi-local in the conformal factor σ and involve the Green’s functions of the massless Dirac operator and the renormalized Green’s function, but for the background metric only, and certain area-like parameters related to the zero-modes.

Magnetohydrodynamic boundary conditions for the two-dimensional fermion gas

Magnetohydrodynamic boundary conditions for the two-dimensional fermion gas

2D Fermionic SPT with CRT symmetry

An invariant of SPT-phases with on-site finite group G symmetry for two-dimensional Fermion systems is derived in the work of Ogata [Commun. Math. Phys. 395(1), 405–457 (2022)]. This invariant is doubled compared to the conjectured one from the invertible quantum field theory. We show that if we require CRT-symmetry (which holds automatically in quantum field theory) in addition, then our invariant reduces to the conjectured one.

Operator solution of the light-front Thirring-Wess model

We present an operator solution of the Thirring-Wess model, formulated and quantized in terms of light-front (LF) variables. The model describes a system of massless fermions interacting with massive vector bosons in two space-time dimensions. An important ingredient of the solution is a consistent quantization of the two-dimensional massless LF fermion field. The field equations are solved exactly on an operator level and the quantum LF Hamiltonian is derived in terms of independent field variables. The axial anomaly and the interacting correlation functions are computed nonperturbatively from the operator solution. An analogous operator solution in the conventional field theory is briefly described for comparison. While in the LF case the ``empty'' Fock vacuum is the lowest-energy eigenstate of the full Hamiltonian, the corresponding Hamiltonian in the conventional theory has to be diagonalized in order to find the true physical ground state, which is a dynamical state with a complicated structure. A comment concerning a recently discussed equivalence between the LF and conventional form of field theory concludes the paper.

Quantum-well states at the surface of a heavy-fermion superconductor

Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1–4). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands2,5–10. Their energy-level separation is typically hundreds of meV (refs. 3,6,11). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states12,13. Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu2Si2, which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.

A two-dimensional tunable double Weyl fermion in BL-α borophene.

Two-dimensional (2D) materials with nontrivial band crossings, namely linear or double Weyl points, have been attracting tremendous attention. However, it remains a challenge to find existing 2D materials that host such nontrivial states. Here, based on first-principles calculations and symmetry analysis, we discover that the recently synthesized BL-α borophene is a metal with a tunable double Weyl point. Remarkably, both bands forming the double Weyl point have upward band bending. In addition, it shows an anisotropic band dispersion when away from the double Weyl point. To characterize its anisotropy, we define a quantity G, which could be changed from 1 to infinity when going from the energy of the double Weyl point to the Fermi level. Furthermore, the outer band of the double Weyl point is sensitive to biaxial strain, and could be changed from upward bending to downward bending. During this process, it has a critical case, in which the outer-band becomes flat. The changes in outer-band induce a variation in the density of states around the double Weyl point, thus giving rise to changes in its macroscopic physical properties. Applying a uniaxial strain enables the double Weyl point to transform into a pair of Weyl points by breaking the threefold rotation of BL-α borophene. When breaking the inversion symmetry and in-plane twofold rotation symmetry by a vertical symmetry, the double Weyl point still persisted; meanwhile, an additional pair of linear Weyl points appears on the high-symmetry path, giving rise to a Weyl complex case. Overall, our work thus provides an existing 2D material, BL-α borophene, to study the nontrivial band crossings in 2D.

Pairing of fermions under spin-orbit coupling in two dimensions

We present a theoretical approach to the problem of two-dimensional fermion pairing under spin-orbit (SO) coupling and Zeeman interaction with an external magnetic field. We introduce a generic pairing Hamiltonian operating in the Hilbert space spanning free pairs and bare two-body bound states. The SO coupling of Rashba or Dresselhaus type provides $p$-wave dressing of an $s$-wave spin-singlet bound state by continua in the triplet scattering channels. In the strong-coupling (Bose-Einstein condensate) limit of the many-body fermion system at zero temperature our theory maps onto the two-channel Fano-Anderson model of a spinless resonant $p$-wave superfluid.

Fingerprints of magnetoinduced charge density waves in monolayer graphene beyond half filling

A charge density wave is a condensate of fermions, whose charge density shows a long-range periodic modulation. Such charge density wave can be principally described as a macroscopic quantum state and is known to occur by various formation mechanisms. These are the lattice deforming Peierls transition, the directional, fermionic wave vector orientation prone Fermi surface nesting or the generic charge ordering, which in contrast is associated solely with the undirected effective Coulomb interaction between fermions. In two-dimensional Dirac/Weyl-like systems, the existence of charge density waves is only theoretically predicted within the ultralow energy regime at half filling. Taking graphene as host of two-dimensional fermions described by a Dirac/Weyl Hamiltonian, we tuned indirectly the effective mutual Coulomb interaction between fermions through adsorption of tetracyanoquinodimethane on top in the low coverage limit. We thereby achieved the development of a novel, low-dimensional dissipative charge density wave of Weyl-like fermions, even beyond half filling with additional magneto-induced localization and quantization. This charge density wave appears both, in the electron and the hole spectrum.

Towards a complete classification of nonchiral topological phases in two-dimensional fermion systems

In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang, and Wen, the concept of equivalence classes of fermionic local unitary (FLU) transformations was proposed to systematically understand nonchiral topological phases in 2D fermion systems and an incomplete classification was obtained. On the other hand, the physical picture of fermion condensation and its corresponding super pivotal categories give rise to a generic mathematical framework to describe fermionic topological phases of quantum matter. In particular, it has been pointed out that in certain fermionic topological phases, there exists the so-called q-type anyon excitations, which have no analogues in bosonic theories. In this paper, we generalize the Gu, Wang, and Wen construction to include those fermionic topological phases with q-type anyon excitations. We argue that all nonchiral fermionic topological phases in $2+1\mathrm{D}$ are characterized by a set of tensors $({N}_{k}^{ij},{F}_{k}^{ij},{F}_{kln,\ensuremath{\chi}\ensuremath{\delta}}^{ijm,\ensuremath{\alpha}\ensuremath{\beta}},{n}_{i},{d}_{i})$, which satisfy a set of nonlinear algebraic equations parameterized by phase factors ${\mathrm{\ensuremath{\Xi}}}_{kl}^{ijm,\ensuremath{\alpha}\ensuremath{\beta}}$ and ${\mathrm{\ensuremath{\Xi}}}_{kln,\ensuremath{\chi}\ensuremath{\delta}}^{ij}$. Moreover, consistency conditions among algebraic equations give rise to additional constraints on these phase factors, which allow us to construct a topological invariant partition for an arbitrary triangulation of 3D spin manifold. Finally, several examples with q-type anyon excitations are discussed, including the fermionic topological phase from Tambara-Yamagami category for ${\mathbb{Z}}_{2N}$, which can be regarded as the ${\mathbb{Z}}_{2N}$ parafermion generalization of Ising fermionic topological phase.

Bond-weighting method for the Grassmann tensor renormalization group

Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group algorithm. The bond weight is controlled by a single hyperparameter, whose optimal value is estimated in the original work via the numerical computation of the two-dimensional critical Ising model. We develop this bond-weighted tensor renormalization group algorithm to make it applicable to the fermionic system, benchmarking with the two-dimensional massless Wilson fermion. We show that the accuracy with the fixed bond dimension is improved also in the fermionic system and provide numerical evidence that the optimal choice of the hyperparameter is not affected by whether the system is bosonic or fermionic. In addition, by monitoring the singular value spectrum, we find that the scale-invariant structure of the renormalized Grassmann tensor is successfully kept by the bond-weighting technique.

Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of gap-closing nodes at the Fermi energy ($E_F$) with other nodes below $E_F$. As the number of linked nodes can be changed only via pair-creation or pair-annihilation, a linked node is more stable and robust than ordinary nodes without linking. Here we propose a new type of a linked nodal structure between a nodal line (nodal surface) at $E_F$ with another nodal line (nodal surface) below $E_F$ in two-dimensional (three-dimensional) spinless fermion systems with $\mathcal{IT}$ symmetry where $\mathcal{I}$ and $\mathcal{T}$ indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, thus the pair are unremovable via a Lifshiftz transition, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight binding model and effective theory are developed for such a linking structure. Also, using density functional theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekul\'{e} texture, as a candidate system hosting the new type of the linked nodal structure.

An Invariant of Symmetry Protected Topological Phases with On-Site Finite Group Symmetry for Two-Dimensional Fermion Systems

We consider SPT-phases with on-site finite group G symmetry for two-dimensional Fermion systems. We derive an invariant of the classification.

Network-Initialized Monte Carlo Based on Generative Neural Networks

We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical observables, irrespective of the system locating at the classical critical point, fermionic Mott insulator, Dirac semimetal, or quantum critical point. We further propose a network-initialized Monte Carlo scheme based on such neural networks, which provides independent samplings and can accelerate the Monte Carlo simulations by significantly reducing the thermalization process. We demonstrate the performance of our approach on the two-dimensional Ising and fermion Hubbard models, expect that it can systematically speed up the Monte Carlo simulations especially for the very challenging many-electron problems.

Graphene\u2019s non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.